In the FAQ, some cards, like Hades (1-046U ハーデス) mention a need to have valid targets when the card is used. This entry also implies that some targets may become invalid before resolution time. This implies that targets are chosen at cast time. However, in the official rules, the only place where choosing a target seems to be mentioned deals with thing happening at resolution time (18.104.22.168.1.). Since there's no special rules mentioning it, this implies that choosing a target is just part of the effect and so is done at resolution time.
I don't know how to resolve this. When is the choosing of a target supposed to take place?